000			04275nam a22004693i 4500
001			EBC5990837
003			MiAaPQ
005			20240724114049.0
006			m o d |
007			cr cnu||||||||
008			240724s2019 xx o ||||0 eng d
020			_a9781470453992 _q(electronic bk.)
020			_z9781470436476
035			_a(MiAaPQ)EBC5990837
035			_a(Au-PeEL)EBL5990837
035			_a(OCoLC)1130902668
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA613.6 _b.L67 2019
100	1		_aLorscheid, Oliver.
245	1	0	_aQuiver Grassmannians of Extended Dynkin Type _d _ Part I : _bSchubert Systems and Decompositions into Affine Spaces.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2019.
264		4	_c©2019.
300			_a1 online resource (90 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.261
505	0		_aCover -- Title page -- Introduction -- Chapter 1. Background -- 1.1. Coefficient quiver -- 1.2. Schubert decompositions -- 1.3. Representations of Schubert cells -- Chapter 2. Schubert systems -- 2.1. The complete Schubert system -- 2.2. Partial Evaluations -- 2.3. Contradictory -states -- 2.4. Definition of -states -- 2.5. The reduced Schubert system -- 2.6. Computing -states -- 2.7. Solvable -states -- 2.8. Extremal edges -- 2.9. Patchwork solutions -- 2.10. Extremal paths -- Chapter 3. First applications -- 3.1. The Kronecker quiver -- 3.2. Dynkin quivers -- Chapter 4. Schubert decompositions for type ̃ _{ } -- 4.1. Contradictory of the first and of the second kind -- 4.2. Automorphisms of the Dynkin diagram -- 4.3. Bases for some indecomposable representations -- 4.4. The main theorem -- Chapter 5. Proof of Theorem 4.1 -- 5.1. Defect -1 -- Appendix A. Representations for quivers of type ̃ _{ } -- A.1. Reflections and Auslander-Reiten translates -- A.2. Indecomposable and exceptional representations -- A.3. The Auslander-Reiten quiver -- A.4. The tubes -- A.5. Roots -- A.6. The defect -- Appendix B. Bases for representations of type ̃ _{ } -- B.1. Defect -1 -- B.2. Defect -2 -- B.3. Positive defect -- B.4. Exceptional tubes of rank 2 -- B.5. Exceptional tubes of rank -2 -- B.6. Homogeneous tubes -- Bibliography -- Back Cover.
520			_aLet Q be a quiver of extended Dynkin type \widetilde{D}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrm{Gr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underline{e} and every indecomposable representation M of defect -1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of \mathrm{Gr}_{underline{e}}(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aDynkin diagrams.
650		0	_aGrassmann manifolds.
650		0	_aMathematics.
655		4	_aElectronic books.
700	1		_aWeist, Thorsten.
776	0	8	_iPrint version: _aLorscheid, Oliver _tQuiver Grassmannians of Extended Dynkin Type _d _ Part I: Schubert Systems and Decompositions into Affine Spaces _dProvidence : American Mathematical Society,c2019 _z9781470436476
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5990837 _zClick to View
999			_c15197 _d15197